Most engineering systems can be accurately simulated using models consisting of Partial Differential Equations. Thus the challenging problem of PDE-constrained optimization arises naturally in engineering design. Issues surface due to the high number of variables involved and the use of specialized software for simulation which may not include an optimization option. In this work we present a methodology for the steady-state optimization of systems for which an input/output steady-state simulator is available. The proposed method is efficient for dissipative systems and is based on model reduction. This framework employs a two-step projection scheme, first onto the low-dimensional, adaptively computed, dominant subspace of the system and second onto the subspace of independent variables. Hence only low order Jacobian and Hessian matrices are used in this formulation, computed efficiently with directional perturbations. (C) 2011 Elsevier Ltd. All rights reserved.